Dombrowski got his start as an administrative assistant in the Chicago White Sox front office in 1978. He was their farm director in 1980 and the assistant GM from 1982 to 1986. He moved to the Expos as farm director in 1987, assistant GM in 1988 and GM from 1988 to 1991, when he was considered a "boy wonder", as very young General Managers were extremely rare at the time (he was just 32 when he took over for Bill Stoneman). During his time with the Expos, he was known for making aggressive trades, something Stoneman had shied away from; one of them would become infamous, as in a bid to win a division title in 1989, he traded the team's top three pitching prospects to the Seattle Mariners in order to acquire P Mark Langston. Langston pitched well the rest of the way, but the Expos fell well short of the postseason; then Langston left as a free agent after the season. What made the deal really hurt is that one of the three pitchers he gave up was a young Randy Johnson, who would turn into a Hall of Famer and 300-game winner.

He was the general manager of the Marlins from 1992 to 2001. During his time in Florida he first put together the 1997 World Series team and then blew it up in a Fire Sale before the celebratory champagne had dried off, ordered to so by ownership. He joined the Tigers as club President in 2001 and added the title of General Manager in 2002.

The Tigers had their worst-ever season in 2003 when they lost 119 games, but soon turned things around under Dombrowski's leadership. One of his first key moves was to convince free agent catcher Ivan Rodriguez to join the woeful team in 2004, and also persuading Jim Leyland, who had managed the Marlins to a world championship under Dombrowski in 1997, to become the team's manager in 2006. The rebuilt Tigers went all the way to the World Series that season, losing to the St. Louis Cardinals and remained in contention for the next decade. Dombrowski orchestrated a number of great trades, particularly the one that brought over 1B Miguel Cabrera who became a superstar in Detroit, and also signed some very productive players as free agents, most notably Victor Martinez. His signing of free agent 1B Prince Fielder before the 2012 season was key to the Tigers returning to the World Series that year, but they were swept by the San Francisco Giants and Fielder's huge contract soon became an albatross. However, he managed to get out from under that by trading him for 2B Ian Kinsler after the 2013 season. With Cabrera and ace pitchers Justin Verlander and Max Scherzer, another great acquisition via trade, all at their peak, the Tigers made a push to return to the World Series in 2014, the first season under new manager Brad Ausmus, by acquiring ace pitcher David Price at the trading deadline, but they were swept by the Baltimore Orioles in the Division Series. Scherzer left as a free agent after the season, and while the Tigers expected to compete again in 2015 and started off the season red hot, they soon ran into injury problems, with Cabrera and Verlander missing long stretches and Victor Martinez not performing up to his standards. As they were struggling to play .500 at the trading deadline, Dombrowski decided to re-tool, trading Price, closer Joakim Soria and LF Yoenis Cespedes at the end of July. On August 4th, owner Mike Ilitch announced that Dombrowski had been released from his contract and that he was being replaced by Al Avila, ending a 14-season stay. Dombrowski's contract was up at the end of the year, and speculation was that Ilitch was not prepared to pay top dollar to retain his services.

To say that Dombrowski did not stay unemployed long would be an understatement. On August 18, 2015, the Boston red Sox surprised everyone by announcing that they had hired him as Vice-President of baseball operations, starting immediately. The hiring came only a couple of weeks after team President Larry Lucchino had announced his impending retirement, and was followed the same day by GM Ben Cherington handing in his resignation. Dombrowski had stated that he wanted Cherington to stay on, but the young executive clearly did not want to play second fiddle to Dombrowski who thus effectively took over full responsibility for reshaping the Red Sox, who were headed to their third last-place finish in four years, the exception being what was starting to look increasingly like a freakish World Series in title in 2013. The Red Sox had a lot of talented young players around the organization, and Dombrowski's first task was to figure out which of those should form the core of the team in the coming years. He also indicated that he would recruit a new GM, as it was his plan to shape the team's future from a higher level within the organization. On September 24th, he introduced Mike Hazen as the team's new GM, and the following day hired Frank Wren, who had worked for him in both the Expos and Marlins organizations as Vice-President in charge of baseball operations, to give his young new GM an experienced mentor to help him out. The Red Sox then turned things around quickly. Dombrowski once again brought David Price on board, this time through free agency, and with a number of young players developed from within the organization, such as Mookie Betts, Jackie Bradley and Xander Bogaerts, taking a step f. as Dombrowski continued to pull the strings, orchestrating a big trade that landed another top-line starting pitcher in Chris Sale.